Turbomachine and turbomachine stage

ABSTRACT

A turbomachine stage including guide vanes, radially inner and/or radially outer airfoil platforms, which together form a guide vane cascade, and further including rotor blades, radially inner and/or radially outer airfoil platforms, which together form a rotor blade cascade adjacent to the guide vane cascade. Radially outer airfoil platforms have cascade regions extending between circumferentially adjacent airfoils, and gap regions which radially and/or axially bound an axial gap extending axially between the guide vane cascade and the rotor blade cascade. A contour of at least one of these gap regions varies, in particular periodically, in the radial and/or axial direction around the circumference.

This claims the benefit of European Patent Application EP 11194433.6, filed Dec. 20, 2011 and hereby incorporated by reference herein.

The present invention relates to a turbomachine, in particular a gas turbine, preferably an aircraft engine gas turbine, having at least one turbomachine stage, in particular a compressor stage or a turbine stage, including a guide vane cascade and a rotor blade cascade, and to such a turbomachine stage.

BACKGROUND

A turbomachine stage has a cascade of rotating rotor blades and a cascade of guide vanes disposed adjacent to the rotor blade cascade on the upstream or downstream side. The rotor blades terminate in a radially outer airfoil platform at the root end. Similarly, guide vanes may be provided at the tip end with a radially outer airfoil platform, for example, in the form of a shroud.

An axial gap is formed between the guide vane cascade and the rotor blade cascade. When the rotor blade cascade rotates, pressure gradients are formed therein, the pressure gradients varying around the circumference and causing secondary flows. For example, a rotating cascade of turbine rotor blades may force working fluid into the axial gap on its pressure side and, conversely, draw working fluid from the gap on its suction side. As a result, a compensating flow is generated, which degrades the efficiency of the turbomachine.

A gas turbine having shroudless rotor blades is disclosed in EP 2 372 102 A2, which proposes that the radially inner platforms of guide vanes and rotor blades have a non-axisymmetric contour, in particular a radially and/or axially undulated contour.

European Patent Publication EP 2 136 033 A1 discloses a turbomachine stage having guide vanes which, together with radially inner and/or radially outer airfoil platforms, form a guide vane cascade. The turbomachine further has rotor blades which, together with radially inner and/or radially outer airfoil platforms, form a rotor blade cascade. Provided between the guide vane cascade and the rotor blade cascade is an axial gap which is bounded by gap regions of the airfoil platforms of the rotor blade cascade and the guide vane cascade. In this connection, only the contour of the gap region of the airfoil platform of the rotor blade cascade varies in the radial and/or axial direction around the circumference.

European Patent Publication EP 1 067 273 A1 describes a turbomachine stage having a rotor blade. The radially outer airfoil platform associated with the rotor blade has a contour which varies in the axial direction, while the radially outer airfoil platform associated with a guide vane has a contour which does not vary in the axial direction.

SUMMARY OF THE INVENTION

It is an object of the present invention to improve the efficiency of a turbomachine, in particular an aircraft engine gas turbine.

A turbomachine stage according to the present invention includes a plurality of rotor blades which are preferably equidistantly distributed around the circumference and, at their root or rotor end, are connected to, in particularly integrally formed with, radially inner airfoil platforms. At their tip or casing ends, the rotor blades may be connected to, in particularly integrally formed with, radially outer airfoil platforms. Rotor blades may be removably or non-removably attached to, in particular integrally formed with, a rotor (member) of the turbomachine, either individually or in groups.

On the upstream and/or downstream side(s) of the cascade formed by these rotor blades, a plurality of guide vanes are preferably equidistantly distributed around the circumference and removably or non-removably attached to, in particular integrally formed with, a casing (member) of the turbomachine. To this end, the guide vanes are connected to, in particular integrally formed with, radially outer airfoil platforms. At their tip or rotor ends, the guide vanes may be connected to, particularly integrally formed with, radially inner airfoil platforms.

At their tip or rotor ends, the guide vanes may be connected to, in particular integrally formed with, radially inner airfoil platforms.

Platform regions extending axially between the airfoil leading and trailing edges and circumferentially between adjacent airfoils, together with the airfoils themselves and, possibly, casing or rotor surface regions, define flow channels for the working fluid, and thus the rotor blade cascade or guide vane cascade, respectively. Therefore, these platform regions are hereinafter referred to as cascade regions.

However, the airfoil platforms may extend axially beyond these cascade regions on the upstream and/or downstream side(s); i.e., beyond the airfoil leading and/or trailing edges. These regions of the airfoil platforms bound an axial gap extending axially between the guide vane cascade and the rotor blade cascade and, therefore, are hereinafter collectively referred to as gap regions of the airfoil platforms.

An airfoil platform may have radially outer gap regions including a plurality of sections. For example, the radially outer airfoil platforms of a rotor blade cascade or a guide vane cascade may have one or more radial shoulders whose circumferential surfaces bound the axial gap radially and whose end faces bound the axial gap axially. In the case of such radially outer gap regions having a plurality of sections, the following explanations may refer to one or more, in particular to all of the sections of a gap region. Thus, for example, when the description speaks of a variation of a radially outer gap region in the radial and/or axial direction, the contour(s) of one or more circumferential surfaces may vary in the radial direction and/or the contour(s) of one or more end faces may vary in the axial direction.

If, in a preferred embodiment, rotor blade tips or shrouds are, in particular sealingly, disposed in a recess of the casing, the casing member in which the recess is formed may form a radially outer gap region of the guide vane platforms according to the present invention. Similarly, a radially outer rotor blade platform which may be disposed in particular in a recess of the casing may form a gap region according to the present invention.

In general, a component which is radially outwardly connected to, or integrally formed with, at least one guide vane or rotor blade and whose contour, possibly together with additional contours, radially and/or axially bounds the axial gap between the rotor blade cascade and the guide vane cascade, may constitute a radially outer gap region of an airfoil platform according to the present invention.

In accordance with the present invention, a contour of one or more of these gap regions varies in the radial and/or axial direction around the circumference. A variation in the radial direction is understood, in particular, to be an outside radius R of the contour which, in polar coordinates, varies with the circumferential angle φ around the axis of rotation of the turbomachine stage, and analogously, a variation in the axial direction is understood, in particular, to be an axial coordinate X of the contour which varies with the circumferential angle. Preferably, the contour varies periodically, in particular sinusoidally:

R(φ)=R ₀ +ΔR×sin(Ω_(R)×φ+Φ_(R))and/or

X(φ)=X ₀ +ΔX×sin(Ω_(x)×φ+Φ_(x)),

where

φε[0°,360°],R ₀ ,ΔR,X ₀ ,ΔX,Ω _(R),Ω_(x),Φ_(R),Φ_(x)=const.

or asymmetrically.

As explained above, this variation (hereinafter also referred to as undulation) may be formed solely in the radial direction, solely in the axial direction, or in both the axial and radial directions. For example, the contour of a cylindrical gap region having a smooth end face and an undulated circumferential surface varies solely in the radial direction, that of a cylindrical gap region having an undulated end face and a smooth circumferential surface varies solely in the axial direction, while that of a cylindrical gap region having an undulated end face and an undulated circumferential surface and that of conical gap region having an undulated circumferential surface vary in both the axial and radial directions.

The undulation may be formed solely on one or more gap regions of radially outer guide vane platforms, solely on one or more gap regions of radially outer rotor blade platforms, or also on one or more gap regions of radially outer platforms of both guide vanes and rotor blades. In a preferred refinement, an undulation may additionally be provided on one or more gap regions of radially inner guide vane platforms and/or on one or more gap regions of radially inner rotor blade platforms.

In a preferred embodiment, a contour of a gap region of an airfoil platform of one of the guide vane and rotor blade cascades and an axially and/or radially opposite contour of a gap region of an airfoil platform of the other of the guide vane and rotor blade cascades may vary around the circumference, preferably identically, in particular in parallel, or with a phase offset of preferably at least 45°, in particular at least 90°, preferably at least 135° and/or preferably of no more than 270°, in particular no more than 210°, and preferably no more than 180°.

If a gap region has two opposite contours, such as an inner and an outer circumferential surface of an annular flange such as, in particular, a shroud extension, or on a casing, then these two opposite contours may vary around the circumference, preferably differently or identically, in particular in parallel, or with a phase offset of preferably at least 45°, in particular at least 90°, preferably at least 135° and/or preferably of no more than 270°, in particular no more than 210°, and preferably no more than 180°. If the two contours vary in parallel, the wall thickness of this gap region of the airfoil platform remains constant. It may equally be provided that only one of such opposite contours, in the case of an annular-flange-like shroud extension preferably the radially inner contour, varies while the other remains constant around the circumference.

In general, an entire contour of a gap region, for example, the entire inner circumferential surface of an annular flange, may vary around the circumference. It is equally possible that only a section of the contour has an undulation. For example, the inner circumferential surface of an annular flange may vary in the radial direction only in one or more axial sections, or an end face may vary in the axial direction only in one or more radial sections.

A radial variation of a contour of a gap region of an airfoil platform of a cascade may be constant in the axial direction, so that troughs and crests are oriented parallel to the axis of rotation of the turbomachine stage. Equally, a radial variation of a contour of a gap region of an airfoil platform of a cascade may also vary in the axial direction, so that troughs and crests extend at an angle to the axis of rotation. In particular, a phase offset may be provided which varies with the axial position x, preferably linearly:

R(φ,x)=R ₀ +ΔR×sin(Ω_(R)×φ+Φ_(R) ×x)

Similarly, an axial variation of a contour of a gap region of an airfoil platform of a cascade may be constant in the radial direction, so that troughs and crests are oriented perpendicularly to the axis of rotation of the turbomachine stage. Equally, an axial variation of a contour of a gap region of an airfoil platform of a cascade may also vary in the radial direction, so that troughs and crests are inclined at an angle to the axis of rotation. Here, too, a phase offset may be provided which varies with the radial position r, preferably linearly:

X(φ,x)=X ₀ +ΔX×sin(Ω_(x)×φ+Φ_(x) ×x)

In a preferred embodiment, in addition to at least one gap region, the cascade region of the airfoil platform varies as well, at least partially, around the circumference in one of the ways described above. In an advantageous refinement, a gap region whose contour varies around the circumference merges smoothly into this cascade region, especially in such a way that a trough of the gap region contour merges into a trough of the cascade region, and a crest of the gap region contour merges into a crest of the cascade region. As is customary in the art, the term “smooth transition” is used, in particular, to refer to a transition which has no sharp edges or bends, but which preferably has a continuous curvature.

In a preferred embodiment, an extreme extent; i.e., a maximum or minimum extent of a radially varying contour of a gap region of an airfoil platform of a cascade is circumferentially located in the pressure-side half of the segment between two adjacent airfoil leading edges or in the suction-side half of the segment between two adjacent airfoil trailing edges of the cascade in order to compensate the pressure increases and decreases induced there.

In general, two airfoil leading or trailing edges of a guide vane or rotor blade cascade define a segment therebetween which extends in the circumferential direction and is divided into two halves by the channel center. The segment half adjoining the pressure side of the airfoil is referred to as “pressure-side half”, the other one as “suction-side half” accordingly. These halves define a circumferential angular range in which, according to the present invention, an extreme extent of a varying contour is disposed. Since the varying contour does not lie at the axial height of this segment itself, this segment may be imagined as being displaced parallel to an extension of the mean camber line of the airfoil for the positioning of the extreme extent.

Preferably, a maximum variation in the radial direction of gap region of an airfoil platform of a cascade is no more than 50%, particularly no more than 40% of the pitch of the cascade.

In a preferred embodiment, in addition or as an alternative to the aforementioned positioning of extreme radial extents around the circumference, an extreme; i.e., a maximum or minimum extent of an axially varying contour of a gap region may be circumferentially located in the region of an airfoil edge, in particular circumferentially spaced from the airfoil edge by no more than 25% of the cascade pitch. Here, too, reference is made to the segment which extends between two adjacent airfoil edges, whose arc length defines the cascade pitch, and which may be imagined as being displaced parallel to the extension of the mean camber line of the airfoil. A maximum extent of a guide vane platform in the axial direction extends preferably axially toward the rotor blade cascade and, analogously, a maximum extent of a rotor blade platform in the axial direction extends preferably axially toward the guide vane cascade.

Preferably, a maximum variation in the axial direction of gap region of an airfoil platform of a cascade is no more than 50%, particularly no more than 40% of the pitch of the cascade.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages will become apparent from the dependent claims and the exemplary embodiments. To this end, the drawings show, partly in schematic form, in:

FIG. 1: a developed view of a portion of a gas turbine stage according to the present invention including a guide vane cascade and a rotor blade cascade having radially outer airfoil platforms whose gap region contours vary in the axial direction around the circumference;

FIGS. 2A, 2B: meridional sections at different circumferential positions through a gas turbine stage according to the present invention including a guide vane cascade and a rotor blade cascade having radially outer airfoil platforms whose gap region contour varies in the radial direction around the circumference; and

FIG. 3: a meridional section, similar to those of FIG. 2, through a gas turbine stage according to the present invention, in which a gap region of a radially outer guide vane platform has a recess formed therein for receiving radially outer rotor blade platforms.

DETAILED DESCRIPTION

FIG. 1 shows a developed view of a portion of a gas turbine stage according to the present invention, as seen from an axis of rotation; i.e., viewed from radially inside to radially outside, showing a stationary cascade of guide vanes 1 and, opposite thereto, a rotating cascade of rotor blades 2. The rotation is indicated by a filled vertical arrow, the flow of working fluid is indicated by an empty arrow in the region of the guide vane cascade. This configuration is merely exemplary for purposes of illustration. The present invention may be used equally in turbine and compressor stages, where the guide vane cascade is disposed upstream and/or downstream of the rotor blade cascade.

Integrally formed with airfoils 1, 2 are radially outer airfoil platforms, which are shown from above in FIG. 1; i.e., as viewed from the axis of rotation of the gas turbine stage. Each airfoil may either have a separate airfoil platform, or several or all of the airfoils of a cascade may be connected to, in particular integrally formed with, the same airfoil platform which, in accordance with the present invention, may then be imagined as being divided into separate airfoil platforms associated with the individual airfoils. Therefore, FIG. 1 does not show any airfoil platform boundaries in the circumferential direction (vertically in FIG. 1). The radially outer platforms of guide vanes 1 may be, for example, a part, in particular an integral part, of a casing of a gas turbine (stage), or be attached to such a casing. The radially outer platforms of rotor blades 2 may be, for example, shrouds, in particular interconnected shrouds.

A cascade region 10.1 of the guide vane platforms and a cascade region 20.1 of the rotor blade platforms extend axially between the respective leading edge (left in FIG. 1) and the respective trailing edge (right in FIG. 1), said cascade regions being hatched from top left to bottom right in FIG. 1.

The cascade regions merge axially into respective gap regions 10.2T and 20.2L beyond the respective airfoil leading or trailing edges, said gap regions being hatched from bottom left to top right in FIG. 1. Gap regions 10.2T and 20.2L each have substantially the shape of a radial shoulder whose circumferential surface facing toward the spoke-like pattern of the respective cascade and whose end face facing toward the respective other airfoil cascade radially and axially bound a radially inner axial gap A between the rotor blade cascade and the guide vane cascade.

As can be seen in the developed view of FIG. 1, the contour of this gap region 10.2T, respectively 20.2L, and more particularly its end face facing the respective other airfoil cascade, varies in the axial direction around the circumference; i.e., in the vertical direction in FIG. 1. That is, the generating lines of the end face, which extend from the axis of rotation of the turbomachine to the peripheral edge of the radial shoulder, have different axial positions, so that the end face has a maximum axial extent A_(max) 10, respectively A_(max) 20, toward the respective other airfoil cascade at selected circumferential positions, as measured from a generating line which is axially farthest away from the respective other airfoil cascade. The generating lines may be perpendicular to the axis of rotation of the turbomachine, or inclined thereto at the same angle or at an angle that varies in the circumferential direction. In the exemplary embodiment, the generating lines are perpendicular to the axis of rotation. Their axial position varies sinusoidally around the circumference, so that maximum axial extents A_(max) 20 of gap region 20.2L of the rotor blade platforms are disposed near respective leading edges of rotor blades 2, and maximum axial extents A_(max) 10 of gap region 10.2T of the guide vanes are disposed near respective trailing edges of guide vanes 1, as viewed in the circumferential direction. Maximum extents A_(max) 10 and A_(max) 20 are each 50% of the respective cascade pitch.

With regard to the position in the circumferential direction, instead of making reference to a position of airfoil edges, the channel center, and the like, which position is displaced parallel to the axis of rotation, reference may also be made to a position which is displaced parallel to the extension of the mean camber line of the respective airfoil. For this purpose, the extension of mean camber line 2.1 of rotor blades 2 is indicated by a dot-dash line. It can be seen that the maximum axial extents A_(max) 20 of gap region 20.2L of the rotor blade platforms are still circumferentially located near the so-displaced positions of the leading edges of rotor blades 2.

FIGS. 2A, 2B show meridional sections at different circumferential positions through a gas turbine stage according to the present invention including a guide vane cascade and a rotor blade cascade having radially outer airfoil platforms whose gap region contour varies in the radial direction around the circumference. In particular, this gas turbine stage may be the one described hereinabove with reference to FIG. 1, so that a radial undulation is combined with an axial undulation. Therefore, in the following, reference is made to the above description and only the aspects of the radial undulation will be described. It is equally possible to provide only an axial undulation, as described hereinabove with reference to FIG. 1, or only a radial undulation, such as will be described hereinafter.

FIG. 2A shows a meridional section at a circumferential position where the circumferential surface of gap region 20.2L has a minimum radial extent in a radially outward direction; i.e., in a direction away from the rotor and, analogously, FIG. 2B shows a meridional section at a circumferential position where the circumferential surface of gap region 20.2L has a maximum radial extent. It can be seen that the circumferential surface of gap region 20.2L varies sinusoidally in the circumferential direction with an amplitude AR=(R_(max) 20+R_(min) 20)/2. The maximum positive amplitude; i.e., the maximum radial extent R_(max) 20 in the radially outward direction, is circumferentially located in the pressure-side half of the segment between two successive rotor blade leading edges. Again, the positions in the circumferential direction may be imagined as being displaced parallel to the extension of the mean camber line to the respective axial positions.

It can be seen that the radial undulation varies not only around the circumference (compare FIG. 2A to FIG. 2B), but also in the axial direction (see the horizontal direction in FIG. 2A, 2B), so that the crests and troughs are inclined at an angle to the axis of rotation. In particular, FIG. 2A shows the trough R_(min) 20 sloping upwardly in the direction of the flow, while FIG. 2B shows the crests R_(max) 20 sloping downwardly in the direction of the flow.

Moreover, it can be seen that this radial undulation of gap region 20.2 merges smoothly into a corresponding undulation of cascade region 20.1 between rotor blades 2.

Although not shown, in addition or as an alternative to the above-described axial undulation (see FIG. 1), the gap region 10.2T of the guide vane platforms, which faces the rotor blade cascade, may also have a radial undulation, such as described hereinabove with reference to gap region 20.2 of the rotor blade platforms.

It can be seen in FIG. 2 that this trailing-edge gap region is shaped like an annular flange, and therefore has two radially opposite surfaces (upper and lower in FIG. 2). A radial undulation may in particular be provided on the radially inner surface (lower in FIG. 2) or on both surfaces. In the latter case, preferably, they vary identically, so that the wall thickness of the annular flange remains constant.

FIG. 3 shows, in a view similar to that of FIG. 2, a portion of a gas turbine stage according to a modified embodiment of the present invention. Corresponding elements are identified by the same reference numerals, so that reference is made to the above explanations in their entirety, and only the differences in the modified embodiment will be discussed below.

Firstly, FIG. 3 shows the downstream trailing edge of a rotor blade 2 and the upstream leading edge of a following guide vane 1. Accordingly, the radially outer gap regions are designated 20.2T (for trailing edge) and 10.2L (for leading edge, and further with an M or S designation as discussed below) to illustrate by way of example that the explanations are equally applicable to leading and trailing edges of rotor blade platforms and guide vane platforms, respectively.

Secondly, the radially outer airfoil platforms are inclined at an angle to the turbine axis to illustrate a divergent flow channel. The explanations apply equally to convergent flow channels (not shown), in particular in compressor stages.

Moreover, the radially outer rotor blade platform, which is in the form of a shroud, has an annular flange formed in its trailing-edge gap region 20.2T. This annular flange has radially opposite circumferential surfaces, such as described hereinbefore with reference to trailing-edge gap region 10.2T of guide vane 1 of FIG. 1. Trailing-edge gap region 20.2T may also have an undulation, in particular the same undulation, on its radially inner (lower in FIG. 3) and/or outer circumferential surface.

The leading-edge gap region includes a radially inner annular flange in a radially outer groove-like recess of the gas turbine casing. Accordingly, the leading-edge gap region has three circumferential surfaces 10.2LM, namely the radially inner and radially outer circumferential surfaces of the annular flange and the circumferential surface of the recess itself, as well as two end faces 10.2LS, namely that of the annular flange and that of the recess itself.

Each of these sections 10.2LM, 10.2LS may have an undulation in the radial direction (10.2LM) and in the axial direction (10.2LS), respectively. Moreover, it is possible that several, in particular all, sections of the gap region have an undulation. In this regard, the modification shown in FIG. 3 is intended to illustrate in one view different variants where a contour of a gap region may vary in the radial and/or axial direction around the circumference.

LIST OF REFERENCE NUMERALS

-   1 guide vane -   2 rotor blade -   2.1 extension of the mean camber line -   10.1/20.1 cascade region of the radially outer airfoil platform of     the rotor blade or guide vane cascade -   10.2T trailing-edge gap region of the radially outer airfoil     platform of the guide vane cascade -   10.2LM circumferential surface section of the leading-edge gap     region of the radially outer airfoil platform of the guide vane     cascade -   10.2LS end face section of the leading-edge gap region of the     radially outer airfoil platform of the guide vane cascade -   20.2T trailing-edge gap region of the radially outer airfoil     platform of the rotor vane cascade -   20.2L leading-edge gap region of the radially outer airfoil platform     of the rotor vane cascade -   A axial gap 

What is claimed is:
 1. A turbomachine stage comprising: guide vanes; a radially outer guide vane airfoil platform defining with the guide vanes a guide vane cascade, the radially outer guide vane airfoil platform having a guide vane cascade region and a guide vane gap region extending axially beyond the guide vane cascade region; rotor blades; a radially outer rotor vane airfoil platform defining with the rotor blades a rotor blade cascade, the radially outer rotor vane airfoil platform having a rotor vane cascade region and a rotor vane gap region extending axially beyond the rotor vane cascade region; the rotor blade cascade being adjacent to the guide vane cascade, the guide vane gap region and the rotor vane gap region at least one of radially and axially defining an axial gap extending axially between the guide vane cascade and the rotor blade cascade; a contour of at least one of the guide vane gap region and the rotor vane gap region varying in at least one of the radial and the axial direction around a circumference, and an at least one of axially and radially opposite contour of the other of the guide vane gap region and the rotor vane gap region varying around the circumference.
 2. The turbomachine stage as recited in claim 1 wherein the contour and the opposite contour are radially opposite.
 3. The turbomachine stage as recited in claim 2 wherein the contour and the opposite contour vary identically.
 4. The turbomachine stage as recited in claim 1 wherein the contour varies both radially and axially.
 5. The turbomachine as recited in claim 1 wherein the contour varially radially but is constant in the axial direction.
 6. The turbomachine stage as recited in claim 1 wherein at least one of the guide vane or rotor vane gap region merges smoothly into the respective guide vane or rotor vane cascade region.
 7. The turbomachine stage as recited in claim 1 wherein the contour varies radially and an extreme extent of the radially varying contour is circumferentially located in a pressure-side half of a segment between two respective adjacent airfoil leading edges or in a suction-side half of a segment between two respective adjacent airfoil trailing edges.
 8. The turbomachine stage as recited in claim 1 wherein the contour varies radially and a maximum variation in the radial direction of the respectve guide vane or rotor vane gap region is no more than 50% of the pitch of the respective guide vane or rotor vane cascade.
 9. The turbomachine as recited in claim 8 wherein the maximum variation is no more than 40%.
 10. The turbomachine stage as recited in claim 1 wherein the contour varies axially and wherein an extreme extent of the axially varying contour is circumferentially located in the region of a respective airfoil edge.
 11. The turbomachine as recited in claim 10 wherein the extreme extent is circumferentially spaced from the respective airfoil edge by no more than 25% of the cascade pitch.
 12. The turbomachine stage as recited in claim 1 wherein the contour varies axially and a maximum variation in the axial direction is no more than 50% the pitch of the respective guide vane or rotor vane cascade.
 13. The turbomachine stage as recited in claim 1 wherein the contour varies periodically.
 14. The turbomachine stage as recited in claim 13 wherein the opposite contour varies identically with the contour.
 15. The turbomachine stage as recited in claim 13 wherein the opposite contour varies identically with the contour.
 16. A turbomachine comprising at least one turbomachine stage as recited in claim
 1. 17. A gas turbine comprising at least one turbomachine stage as recited in claim
 1. 18. An aircraft engine gas turbine comprising at least one turbomachine stage as recited in claim
 1. 19. A compressor stage comprising the turbomachine stage as recited in claim
 1. 20. A turbine stage comprising the turbomachine stage as recited in claim
 1. 